Solve 0.92x+0.98(900-x)/900geq0.94

$$\frac{ 0.92x+0.98(900-x) }{ 900 } \geq 0.94$$

Solve for x

$$x\leq 600$$

Solution Steps

Multiply both sides by 900. Since 900 is positive, the inequality direction remains the same.

$$0.92x+0.98\left(900-x\right)\geq 0.94\times 900$$

Use the distributive property to multiply 0.98 by 900-x.

$$0.92x+882-0.98x\geq 0.94\times 900$$

Combine 0.92x and -0.98x to get -0.06x.

$$-0.06x+882\geq 0.94\times 900$$

Multiply 0.94 and 900 to get 846.

$$-0.06x+882\geq 846$$

Subtract 882 from both sides.

$$-0.06x\geq 846-882$$

Subtract 882 from 846 to get -36.

$$-0.06x\geq -36$$

Divide both sides by -0.06. Since -0.06 is negative, the inequality direction is changed.

$$x\leq \frac{-36}{-0.06}$$

Expand \frac{-36}{-0.06} by multiplying both numerator and the denominator by 100.

$$x\leq \frac{-3600}{-6}$$

Divide -3600 by -6 to get 600.

$$x\leq 600$$